She should be hustling to class, hitting the books, acing tests. In short, she should be climbing that old-school ladder toward a coveted spot among America’s future elite.

She isn’t doing any of that. Instead, Ms. Full, as bright and poised and ambitious as the next Ivy Leaguer, has done something extraordinary for a Princetonian: she has dropped out.

It wasn’t the exorbitant cost of college. (Princeton, all told, runs nearly $55,000 a year.) She says she simply received a better offer — and, perhaps, a shot at a better education.

Ms. Full, 20, is part of one of the most unusual experiments in higher education today. It rewards smart young people for not going to college and, instead, diving into the real world of science, technology and business.

The idea isn’t nuts. After all, Bill Gates and Steve Jobs dropped out, and they did O.K.

Of course, their kind of success is rare, degree or no degree. Mr. Gates and Mr. Jobs changed the world. Ms. Full wants to, as well, and she’s in a hurry. She has built a low-cost solar panel and is starting to test it in Africa.

“I was antsy to get out into the world and execute on my ideas,” she says.

At a time when the value of a college degree is being called into question, and when job prospects for many new graduates are grimmer than they’ve been in years, perhaps it’s no surprise to see a not-back-to-school movement spring up. What is surprising is where it’s springing up, and who’s behind it.

The push, which is luring a handful of select students away from the likes of Princeton, Harvard and M.I.T., is the brainchild of Peter H. Thiel, 44, a billionaire and freethinker with a remarkable record in Silicon Valley. Back in 1998, during the dot-com boom, Mr. Thiel gambled on a company that eventually became PayPal, the giant of online payments. More recently, he got in early on a little start-up called Facebook.

Since 2010, he has been bankrolling people under the age of 20 who want to find the next big thing — provided that they don’t look for it in a college classroom. His offer is this: $50,000 a year for two years, few questions asked. Just no college, unless a class is helpful for their Thiel projects.

A cool hundred grand, no strings attached? You won’t be shocked to learn that it is harder to get a Thiel Fellowship than it is to get into Princeton. Mr. Thiel (Stanford ’89, Stanford Law ’92) has grabbed headlines with his outlandish offer. Less has been said about the handful of plucky people who have actually managed to snag one of his fellowships in hopes of becoming the next Gates or Jobs. The first Thiel fellows are now in their second year of the program. Twenty new ones were selected this summer.